In this paper, we propose an extension of the calibration approach considered in Brigo and Mercurio [Finance Stoch., 2001, 5(3), 369–387] to the multiple-curve setting.We introduce deterministic time shifts in order to match any initial term structure while keeping the time homogeneity of the Markov process driving the instantaneous risk-free spot rate and the spot LIBOR.We apply the methodology to the case where the Markov process belongs to the affine family, where closed form solutions are available for the bond prices and the FRAs on LIBOR. A calibration exercise based on real data illustrates in the simple Gaussian setting the flexibility of our approach, which reveals its potentiality in the non-Gaussian environment, where loosing time homogeneity leads to very uncomfortable consequences in terms of the solvability of the corresponding Riccati ODEs
A flexible spot multiple-curve model
GRASSELLI, MARTINO;MIGLIETTA, GIULIO
2016
Abstract
In this paper, we propose an extension of the calibration approach considered in Brigo and Mercurio [Finance Stoch., 2001, 5(3), 369–387] to the multiple-curve setting.We introduce deterministic time shifts in order to match any initial term structure while keeping the time homogeneity of the Markov process driving the instantaneous risk-free spot rate and the spot LIBOR.We apply the methodology to the case where the Markov process belongs to the affine family, where closed form solutions are available for the bond prices and the FRAs on LIBOR. A calibration exercise based on real data illustrates in the simple Gaussian setting the flexibility of our approach, which reveals its potentiality in the non-Gaussian environment, where loosing time homogeneity leads to very uncomfortable consequences in terms of the solvability of the corresponding Riccati ODEs
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